How Many Dimes?
A woman has in change in her purse, made up entirely of dimes and quarters. Given that there are more quarters than dimes in her purse, what is the total number of dimes?Source: NCTM Mathematics Teacher, November 2006

SOLUTION
Let be the number of quarters and the number of dimes.
Simplify
Since is even, is even which implies that is odd.
If
If
Substitute the value of into Eq.
If , Eq. is also satisfied but with dimes.
The total number of dimes equals .